Pith Number

pith:BMHAKC5G

pith:2016:BMHAKC5G3UXX2NZFQEHM3KNOV6

not attested not anchored not stored refs pending

Macdonald symmetry at $q=1$ and a new class of inv-preserving bijections on words

Jennifer Morse, Maria Gillespie, Ryan Kaliszewski

arxiv:1611.04973 v2 · 2016-11-15 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BMHAKC5G3UXX2NZFQEHM3KNOV6}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:57:36.955732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e

Aliases

arxiv: 1611.04973 · arxiv_version: 1611.04973v2 · doi: 10.48550/arxiv.1611.04973 · pith_short_12: BMHAKC5G3UXX · pith_short_16: BMHAKC5G3UXX2NZF · pith_short_8: BMHAKC5G

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f803cef0b9fb24369ab7fe9f38453ae7096d6db5062c2c589b2858a8074de99",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-15T18:17:15Z",
    "title_canon_sha256": "ce4f57532c57fdc9a053b3e940786d9ff31eb6f477d362eb41551795b2d0bc77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04973",
    "kind": "arxiv",
    "version": 2
  }
}